### Waves - Result Question 9

#### 9. The time of reverberation of a room $A$ is one second. What will be the time (in seconds) of reverberation of a room, having all the dimensions double of those of room A? [2006]

(a) 4

(b) $\frac{1}{2}$

(c) 1

(d) 2

## Show Answer

#### Answer:

Correct Answer: 9. (d)

Solution:

- (d) The time gap between the initial direct note and the reflected note upto the minimum andibility level is called reverberation time.

Sabine has shown that standard reverberation time for an auditorium is given by the formula

$ T_R=K \frac{V}{\alpha S} $

Where, $V$ is volume of the auditorium, $S$ is the surface area. So, $T_R=\frac{K \cdot V}{\alpha S}=1$ (given)

$T_R=\frac{K \cdot l^{3}}{6 \alpha l^{2}}$

(Assuming auditorium to be cubic in shape)

$=\frac{K}{6 \alpha} l$

So, $T_R \alpha l$

If dimension is doubled, reverberation time $t$ will be doubled. So, New $T_R=2 sec$.